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Theorem nfcsb1 3282
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypothesis
Ref Expression
nfcsb1.1  |-  F/_ x A
Assertion
Ref Expression
nfcsb1  |-  F/_ x [_ A  /  x ]_ B

Proof of Theorem nfcsb1
StepHypRef Expression
1 nfcsb1.1 . . . 4  |-  F/_ x A
21a1i 11 . . 3  |-  (  T. 
->  F/_ x A )
32nfcsb1d 3281 . 2  |-  (  T. 
->  F/_ x [_ A  /  x ]_ B )
43trud 1332 1  |-  F/_ x [_ A  /  x ]_ B
Colors of variables: wff set class
Syntax hints:    T. wtru 1325   F/_wnfc 2559   [_csb 3251
This theorem is referenced by:  nfcsb1v  3283  iundisj  19442  disjabrex  24024  disjabrexf  24025  iundisjf  24029  iundisjfi  24152
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-sbc 3162  df-csb 3252
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